Another cool Video but there is a part showing the theatre and what appears to be "Hooray for Hollywood," though the up loader claims this video is from July 1990, which would be during Dick Tracy's run

A more complete version of one of the shows. This uploader claims it's called "Hooray for Hollywood" Which makes sense because the first song is to the tune of it and the finale is a modified version of the song.

"The Theater of the Stars opened on May 1, 1989, with a show entitled Hollywood, Hollywood! That show continued until August 31, 1991. There were three other shows that performed there concurrently—Swing, Swing, Swing (April 7-18, 1990), Dick Tracy Starring in “Diamond Double Cross” (May 21, 1990 to February 16, 1991) and Hollywood’s Pretty Woman (September 24 to November 3, 1991). Beauty and the Beast—Live on Stage opened at the theater on November 22, 1991. This is the full list of shows and their dates, based on the weekly entertainment programs for that period."